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<a href="CAD_using_en.htm">See operating CAD</a>




<h2>Vectors</h2>
Vectors use the identification letter D  (direction).

See also: <a href="CAD_Base_en.htm#D">vector codes</a> (what is a vector ..)
See also: <a href="CAD_Base_en.htm#fmt_dynamic-obj">dynamic vectors</a>





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<a name="F0"></a>
<h2>VEC cartes, polar</h2>
Create vector.

   BaseVector       basevector   see <a href="CAD_input_en.htm#_Vec_">vector</a>
   [Angle-Rot.]     rotation around the z-axis of the active construction-plane
   [Angle-Tilt]     <a href="CAD_Base_en.htm#ANGT">tilting angle</a> in the active construction-plane
   [Length]         Definition of vector <a href="CAD_input_en.htm#_Val_">length</a>
   [REVers]         Reverse Direction ("REV"; also with Page-Down key)


  <B>Definition basevector:</B>
    Definition by entering the components of the axis (eg "0 0 1", a z-vector)

    Or input of a standard vector - eg key in "DX" - 
      or select X- Y- or Z-axis of symbolic-axis-system in left low corner
      Standardvectors are DX DY DZ DIX DIY DIZ - of the absolute coordinate-system,
      DX is 1,0,0; DY is 0,1,0 ..
      - or select X- Y- or Z-axis of symbolic-axis-system in left low corner

    Or a defined vector (eg "D20"; with Page-Up or Down key or select
      from the objectbrowser (left side))

    Or selection of a line or polygonsegment (or polygonsegment in CCV)
      or plane or plain surface.


Examples:
# Vector from X,Y,Z-components:
D20=D(0.7 0 0.7)

# X-Vector rotated 30 deg. around the z-axis of the active construction-plane
#   and then 60 deg. tilted.
D21=DX ANG(30) ANG(60)

# Vector reverted
D22=D21 REV



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<h2>VEC from objects</h2>



Vectors parallel or right-angled to existing objects.

   Obj1              Line or curve or surface
   [Point (on obj)]  basepoint for vector (<a href="CAD_input_en.htm#_PT_">point</a>)
   [PT or VC]        additional object (parallel / normal vector)
   [Length]          Definition of vector length
   [REVers]          Reverse Direction ("REV"; with Page Down key)
   [parallel-across] parallel (tangential (PARL)) or normal (rectangular (CX))



<b>Parallel vector:</b>

  Vector tangential to curve
   Obj1              Line or curve or surface
   [Point (on obj)]  Basepoint of vector on curve / surface
   [Length]
   [REVers] 

  Vector between 2 points
   Obj1              startpoint
   [Point (on obj)]  endpoint
   [Length]
   [REVers] 

  Vector on surface parallel to Isoparametric direction U or V
   - not yet implemented for all surface-types
  Vector X-axis or Y-axis for circle ellipse plane
   Obj1              surface circle ellipse or plane
   [Length]
   [REVers] 
   PARL oder CX      PARL: direction U (along)
                     CX:   direction V (across)
                     none: Normalvector to surface



<b>Normal vector:</b>

  Normalvector to circle ellipse plane surface
   - not yet implemented for all surface-types
   Obj1              circle ellipse plane surface
   [Length]
   [REVers] 

  Normalvector to plane from 2 linear segments (crossproduct):
   Obj1              line or vector
   [PT or VC]        point or vector or vector from line
   [Length]
   [REVers] 

  Normalvector to plane from 3 points (crossproduct):
   Obj1              point on x-axis
   [Point (on obj)]  origin (startpoint for X-axis, Y-axis)
   [PT or VC]        point near Y-axis
   [Length]
   [REVers] 



<b>Vector from plane / reference-system (R):</b>

   Obj1              select user-defined plane
   [PT or VC]        key DX or DY or DZ

   - gives the corresponding axis;
   - result is "D#=R# DX" or "D#=R# DY" or "D#=R# DZ"


Examples:

# Normal vector to circle
D20=C20

# Tangential vector to circle
D21=C20 P(C20 0.2)

# Vector between points P1, P2; length 100.
D5=P1 P2 VAL(100)

# Normal vector to line L20:
D20=L20 DZ

# Vectors of existing Plane:
D20=R20 DX      # X-axis-Vector of plane R20 or D20=R20 PARL or "D(R20 PARL)"
D20=R20 DY      # Y-axis-Vector of plane R20 or D20=R20 CX
D20=R20         # Z-axis-Vector of plane R20 or D20=R20 DZ




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The following commands must be produced manually:

<h2>Vector-Multiplication / Divison</h2>
D21 = D20 * 2
D22 = D20 / 2






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